In the next decade, there will be an exponential increase in the amount of information available about biological structure -ranging from the structure of organs and organisms to the structure of macromolecules. The National Library of Medicine has targeted the representation, management, and manipulation of biological structure as a key element of its mission in the next decade. Biological structure has certain attributes that make its representation and manipulation different from those of other structural domains (such as mechanical engineering). First, the variability in an individual structure over time can be quite large (be it the dynamic motion of a protein molecule, or the changing shape of a beating heart). Second, the range of structures over a population can be large, although the individual structures still share common overall features. Finally, the degree of certainty with which we can learn about biological structure is often a function of imperfect measurement techniques. Since we use our knowledge of biological structure for a variety of critically important tasks (ranging from drug design to medical treatment planning), the representation of biological structure and of that structure's variation is a particularly challenging and important task. The hypothesis of this work is that probabilistic representations of structure are sufficiently expressive to capture a wide range of structural phenomena, and are sufficiently tractable to be useful as a basis for programs that generate, modify, and analyze structure. Building on my previous work in probabilistic structure determination, I present a two-part plan to extend our understanding of structure representation and manipulation in the context of biological macromolecules. In the first part, I will study the theoretical algorithmic and implementational issues that arise when one computes with uncertain structural representations and with uncertain constraints on these representations. In the second part, I will collaborate with other scientists on a set of three important biological-structure problems that not only will provide useful primary scientific results, but also will act to ground the theoretical work in real-world problems.